Koda, Yuya

写真a

Affiliation

Faculty of Economics (Hiyoshi)

Position

Professor

Related Websites

Contact Address

4-1-1, Hiyoshi, Kohoku, Yokohama, 223-8521, Japan

Career 【 Display / hide

  • 2005.04
    -
    2007.09

    JSPS Reasearch Fellow, DC1

  • 2007.10
    -
    2008.03

    JSPS Reasearch Fellow, PD

  • 2008.04
    -
    2008.05

    Keio University, Department of Mathematics, Visiting Scholar

  • 2008.06
    -
    2008.09

    Kogakuin University, Academic Support Center, Lecturer

  • 2008.10
    -
    2009.08

    Tokyo Institute of Technology, Department of Mathematics, Assistant Professor

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Academic Background 【 Display / hide

  • 2000.04
    -
    2003.03

    Keio University, 理工学部, 数理科学科

    University, Graduated

  • 2003.04
    -
    2005.03

    Keio University, 大学院理工学研究科, 基礎理工学専攻

    Graduate School, Completed, Master's course

  • 2005.04
    -
    2007.09

    Keio University, 大学院理工学研究科, 基礎理工学専攻

    Graduate School, Completed, Doctoral course

Academic Degrees 【 Display / hide

  • Ph.D. (Science), Keio University, Coursework, 2007.09

 

Papers 【 Display / hide

  • Positive flow-spines and contact 3-manifolds

    Ishii I., Ishikawa M., Koda Y., Naoe H.

    Annali di Matematica Pura ed Applicata (Annali di Matematica Pura ed Applicata)  202 ( 5 ) 2091 - 2126 2023.10

    ISSN  03733114

     View Summary

    A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. We say that a contact structure on a closed, connected, oriented 3-manifold is supported by a flow-spine if it has a contact form whose Reeb flow is a flow of the flow-spine. It is known by Thurston and Winkelnkemper that any open book decomposition of a closed oriented 3-manifold supports a contact structure. In this paper, we introduce a notion of positivity for flow-spines and prove that any positive flow-spine of a closed, connected, oriented 3-manifold supports a contact structure uniquely up to isotopy. The positivity condition is critical to the existence of the unique, supported contact structure, which is also proved in the paper.

  • Homotopy Motions of Surfaces in 3-Manifolds

    Koda Y., Sakuma M.

    Quarterly Journal of Mathematics (Quarterly Journal of Mathematics)  74 ( 1 ) 29 - 71 2023.03

    ISSN  00335606

     View Summary

    We introduce the concept of a homotopy motion of a subset in a manifold and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behavior of simple loops on a Heegaard surface and monodromies of virtual branched covering surface bundles associated with a Heegaard splitting.

  • Positive flow-spines and contact 3-manifolds, II

    Ishii I., Ishikawa M., Koda Y., Naoe H.

    Annali di Matematica Pura ed Applicata (Annali di Matematica Pura ed Applicata)   2023

    ISSN  03733114

     View Summary

    In our previous paper, it is proved that for any positive flow-spine P of a closed, oriented 3-manifold M, there exists a unique contact structure supported by P up to isotopy. In particular, this defines a map from the set of isotopy classes of positive flow-spines of M to the set of isotopy classes of contact structures on M. In this paper, we show that this map is surjective. As a corollary, we show that any flow-spine can be deformed to a positive flow-spine by applying first and second regular moves successively.

  • Goeritz groups of bridge decompositions

    Susumu Hirose, Daiki Iguchi, Eiko Kin, Yuya Koda

    International Mathematics Research Notices (International Mathematics Research Notices)  IMRN 2022 ( 12 ) 9308 - 9356 2022

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  10737928

     View Summary

    For a bridge decomposition of a link in the 3-sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the 3-sphere that preserve each of the bridge sphere and link setwise. After describing basic properties of this group, we discuss the asymptotic behavior of the minimal pseudo-Anosov entropies. We then give an application to the asymptotic behavior of the minimal entropies for the original Goeritz groups of Heegaard splittings of the 3-sphere and the real projective space.

  • Handlebody decompositions of 3-manifolds and polycontinuous patterns

    Naoki Sakata, Ryosuke Mishina, Masaki Ogawa, Kai Ishihara, Yuya Koda, Makoto Ozawa, Koya Shimokawa

    Proceedings of the Royal Society A (Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)  478 ( 2260 ) 20220073 2022

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  13645021

     View Summary

    We introduce the concept of a handlebody decomposition of a three-manifold, a generalization of a Heegaard splitting, or a trisection. We show that two handlebody decompositions of a closed orientable three-manifold are stably equivalent. As an application to materials science, we consider a mathematical model of polycontinuous patterns and discuss a topological study of microphase separation of a block copolymer melt.

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Research Projects of Competitive Funds, etc. 【 Display / hide

  • 多面体を用いた3・4次元多様体の微分構造と幾何構造の研究

    2021.04
    -
    Present

    文部科学省・日本学術振興会, 科学研究費補助金 基盤研究(C), Principal investigator

  • 多面体を用いた3・4次元多様体の微分構造と幾何構造の研究

    2020.04
    -
    2024.03

    基盤研究(C), Principal investigator

  • 3次元多様体のシャドウ複雑度と幾何構造に関する研究

    2017.04
    -
    2021.03

    文部科学省・日本学術振興会, 科学研究費補助金 基盤研究(C), Principal investigator

  • ヒーガード分解の写像類群の研究

    2014.04
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    2017.03

    文部科学省・日本学術振興会, 科学研究費補助金 若手研究(B), Principal investigator

  • 四面体分割からみた結び目と3次元多様体の不変量の研究

    2009.04
    -
    2013.03

    文部科学省・日本学術振興会, 科学研究費補助金 若手研究(B), Principal investigator

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Courses Taught 【 Display / hide

  • CALCULUS

    2024

  • ADVANCED LINEAR ALGEBRA

    2024

  • INTRODUCTION TO CALCULUS

    2024

  • MATHEMATICS FOR ECONOMICS 2

    2024

  • MATHEMATICS FOR ECONOMICS 1

    2024

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Memberships in Academic Societies 【 Display / hide

  • The Mathematical Society of Japan, 

    2006
    -
    Present

Committee Experiences 【 Display / hide

  • 2024.03
    -
    Present

    Scientific Editor, Journal of Knot Theory and Its Ramifications

  • 2022.04
    -
    2023.03

    理学部数学科長, 広島大学

  • 2022.03
    -
    2023.02

    中国・四国支部 評議員, 日本数学会

  • 2020.04
    -
    2023.03

    Hiroshima Mathematical Journal 編集委員

  • 2016.06
    -
    2020.05

    雑誌『数学』 編集委員, 日本数学会